I am faced with a problem, that I'm pretty sure is a statistical one, but me taking 1 course in probability followed by 1 course in statistics back in university did not prepare me to adequately face it. With that in mind, while a R-based sample code is always helpful and appreciated, what I'm really after is some directions to learn about the problem at large. At the moment I'm at a stage where I'm not really sure what keywords to plug into google :)
So here is the set up (fully computerized simulation, even though objects might suggest physical entities).
- I have a bunch of robots
- The robots share power supply (this is the point of optimization)
- Robots are not identical (further complicates optimization)
- These robots perform various tasks
- The tasks have value assigned to them. Once the task is complete by a robot I can tell how much benefit that brought, but I can't know it ahead of time.
- I have a series of heuristics (H1, H2, ..., Hn) that try to approximate the real performance of a task before it is completed. I use these to decide which task a given robot should perform, obviously these are inaccurate.
From simulations ignoring the shared power supply I have:
- Series representing the true performance of each robot (by letting each robot just do a bunch of tasks, exhaustive enumeration is impossible, so a sampling of possible tasks is used instead)
- Series representing the total system performance (all individual robot performances combined)
- Series corresponding to each heuristic function (a perfect heuristic would be identical to the true performance series, but I don't have one like that)
So what I want to establish are the following 2 things:
- Decide which heuristic functions are better at predicting future performance based on how they did in the simulation window (could be individual functions or combination). The problem here is that it's not a simple combination, since H1 can have values in [0, 1] and H2 in thousands.
- Decide power allocations % for each robot. In real use I'd like to make sure that I use the guiding heuristics (from #1) that ensures that each robot brings the most benefit. I intend to achieve this by insuring that the robot with the most accurate heuristics and the highest predictions of future performance gets the most power. But how much more power? How should I split it? This is the ultimate problem I need to solve.